Problem 15-13 The following payoff table shows profit for a decision analysis pr
ID: 3267915 • Letter: P
Question
Problem 15-13 The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature: State of Nature Decision Alternative S1 S2 S3 d1 250 100 100 d2 200 100 150 The probabilities for the states of nature are P(s1) = 0.45, P(s2) = 0.25, and P(s3) = 0.3. (a) What is the optimal decision strategy if perfect information were available? S1 : S2 : S3 : (b) What is the expected value for the decision strategy developed in part (a)? If required, round your answer to one decimal place. 112.5 (c) Using the expected value approach, what is the recommended decision without perfect information? What is its expected value? If required, round your answer to one decimal place. -137.5 (d) What is the expected value of perfect information? If required, round your answer to one decimal place. -137.5 Just to be clear: the answer to B is NOT 112.5 Answer to C is NOT -137.5 Answer to D is NOT -137.5 please try to be very clear in what the answers are for question B, C and D - I already solved part A
Explanation / Answer
Ans:
a)Optimal decision strategy(if perfect information ere available):
We will choose best pay off in each state of nature.
So,In s1,we will choose d1
In s2,we can choose either of d1 or d2
In s3,we will choose d2
b)Expected value for above strategy=0.45*250+0.25*100+150*0.3=182.5
c)Expected value approach:
Recommended decision without perfect information will be d1(as highest)
d)Expected value of perfect information=Expected value with perfect information -Expected value without perfect information
EVPI=182.5-167.5=15
s1 s2 s3 d1 250 100 100 d2 200 100 150 0.45 0.25 0.3